Polymer electrolyte membrane fuel cells (PEMFC) are devices that produce electricity by means of a chemical reaction between hydrogen and oxygen. These devices are possible alternatives for the replacement of internal combustion engines. However, they are not yet competitive, because their cost, weight and volume are still too large. A challenge is thus to increase PEMFC efficiency by optimizing their design. The main objective of the present project is to develop mathematical and numerical modeling tools in order to optimize the PEMFC design. First, small-scale transport phenomena in the porous media of PEMFC are formulated mathematically, and then a volume averaging method is used to transform these equations into equations that are valid at a larger scale in the porous media. The new mathematical model obtained with this strategy shows that the mass conservation equation contains an additional term, while the momentum equation remains similar to Darcy’s Law. Second, a numerical model is developed in order to optimize the geometry of catalytic channels in which a fluid undergoes chemical reactions. This kind of flow may represent, for example, the reacting species that move in PEMFC channels. Correlations are developed analytically in order to predict the optimal designs for these channels. These correlations were validated with numerical simulations. The results obtained may be applied to several different devices (e.g., microreactors, monolith, PEMFC). Finally, the mathematical and numerical model of a PEMFC are developed and validated. This model is used to optimize catalyst allocation between the anode and cathode sides of the fuel cell, and also to optimize catalyst distribution within the cathode catalyst layer. The analysis shows that an unequal allocation of catalyst between the anode and cathode sides results in a higher electric current. It was also shown that a non-uniform catalyst distribution within the cathode layer yields higher electric current. Finally, the most influential parameters of the numerical model were identified by a sensitivity analysis.